Question

In a meter bridge experiment, the resistance of resistance box is $16\Omega$, which is inserted in right gap. The null point is obtained at $36\text{cm}$ from the left end. The least count of meter scale is $1\text{mm}$. The value of unknown resistance is
(Assume that error in measurement of null point is half of the least count)

• A. $9\pm \frac{5}{128}\Omega$
• B. $9\pm \frac{5}{256}\Omega$
• C. $9\pm \frac{5}{512}\Omega$
• D. $9\pm \frac{1}{2560}\Omega$

Answer 1

The correct option is B $9\pm \frac{5}{256}\Omega$

Using condition for balanced wheat stone bridge,
$\frac{x}{R}=\frac{l}{100-l}$
$\frac{x}{16}=\frac{36}{100-36}$
$x=9\Omega$

For calculating error,
$\frac{\Delta x}{x}=\frac{\Delta l}{l}+\frac{\Delta (100-l)}{100-l}$
$\frac{\Delta x}{x}=\frac{\Delta l}{l}+\frac{\Delta l}{100-l}$
$\Delta x=9\times 0.05(\frac{1}{36}+\frac{1}{64})$
$\Delta x=\frac{9\times 0.05\times 100}{36\times 64}=\frac{5}{256}$
$R=x\pm \Delta x=9\pm \frac{5}{256}$